Commonly used methods for modelling electrical circuits are the Modified Nodal Analysis (MNA) [1]}, the Modified Loop Analysis (MLA) [2]}, or the analysis via Branch-oriented Models (BOM) [3]} (or tree-based formulations) also known as hybrid analysis in the circuit literature [4]}, [5]}, [6]}, [7]}.
It has been shown in [8]}, [9]}, [10]}, [11]} that the index of the DAE resulting from the hybrid analysis is at most one for strictly locally passive components, in contrast to MNA and other nodal techniques, for which certain configurations (as \({\hspace{0.2pt}{\hspace{0.2pt}\texttt {C}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {V}}}\) -cycles or \({\hspace{0.2pt}{\hspace{0.2pt}\texttt {L}}}{\hspace{0.2pt}{\hspace{0.2pt}\texttt {I}}}\) -cutsets) yield index two systems .
